Fish do not need to be slaughtered as a dead fish is still considered permissible. Thus, it is permissible to fish using any means that do not cause harm to the fish. Accordingly, it is permissible to catch fish using an electric shock which does not cause any harm, such as it leading to the death of small fish, affecting the population of fish, or any harm caused to the body, or money of a person, or there is a law illegalizing the catching of fish using this method. If there is none of the above issues then it is permissible. 

It is permissible to eat fish from any method of fishing, apart from methods which are harmful, for example throwing the poison in the sea so that fish die and it is easier to remove them from the water. The Prophet said: Two types of dead animals and two types of bloods have been made lawful for us, the two types of dead animals are locusts and fish (seafood), while the two types of bloods are the liver and the spleen. narrated by Al darqatni. The prophet also allowed his companions to eat a big fish which was dead, found on the coast of the sea, it is said it was a sperm whale. and Allah SWA says: (And whatever the Prophet has given you then accept it, and what he has cautioned you against then avoid it) And Allah speaks the truth, and guides to the straight path. 

As published in the Kuwaiti Encyclopedia of Islamic Jurisprudence;

Animals which are permissible to eat, whether they are fish or locust, there is no need to slaughter them, because the dead fish, and dead locusts are pure and permissible to eat, as Ibn Umar RA narrated: (Two types of dead animals and two types of bloods have been made lawful for us, the two types of dead animals are locusts and fish (seafood), while the two types of bloods are the liver and the spleen) and the saying of the Prophet (It’s water is purifying and its dead (animals) are lawful (to eat).

As for the rest of the sea creatures other than fish, then according to the majority they can be eaten without slaughtering, and according to the Hanafis they are not lawful for human consumption even if they are slaughtered. Everything which does not have blood as such can be eaten by the majority even without slaughtering. However the Malikis have differed on the ruling for creatures which do not have blood, and they said: It is only permissible if it is slaughtered.